1 citations · 2 across the 15 of their papers we have counts for
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On the Bernoulli Numbers via the Newton-Girard Identities
Mario DeFranco
We prove formulas for the Bernoulli numbers by using the Newton-Girard identities to evaluate the Riemann zeta function at positive even integers. To do this, we define a sequence…
On the Multiple Zeta Values
Mario DeFranco
We evaluate the multiple zeta values by proving a certain factorization property. The proof uses a combinatorial bijection and elementary telescoping series. We show h…
On a series for the upper incomplete Gamma function
Mario DeFranco
We define an absolutely convergent series for the upper incomplete Gamma function for and . We express this series using certain polynomials whi…
On the inequalities in Hermite's theorem for a real polynomial to have real zeros
Mario DeFranco
We prove expressions for the inequalities in Hermite's theorem which are conditions for a real polynomial to have real zeros. These expressions generalize the discriminant of a qua…
On properties of the Taylor series coefficients of the Riemann xi function at
Mario DeFranco
We prove some properties about the non-zero Taylor series coefficients of the Riemann xi function at . In particular, we present integral formulas that…
A Constructive Proof of Jacobi's Identity for the Sum of Two Squares
Mario DeFranco
We present a constructive proof of Jacobi's identity for the sum of two squares. We present a combinatorial proof of the Jacobi Triple Product and combine with a proof of Hirschhor…